We study evaluating a policy under best- and worst-case perturbations to a
Markov decision process (MDP), given transition observations from the original
MDP, whether under the same or different policy. This is an important problem
when there is the possibility of a shift between historical and future
environments, due to e.g. unmeasured confounding, distributional shift, or an
adversarial environment. We propose a perturbation model that can modify
transition kernel densities up to a given multiplicative factor or its
reciprocal, which extends the classic marginal sensitivity model (MSM) for
single time step decision making to infinite-horizon RL. We characterize the
sharp bounds on policy value under this model, that is, the tightest possible
bounds given by the transition observations from the original MDP, and we study
the estimation of these bounds from such transition observations. We develop an
estimator with several appealing guarantees: it is semiparametrically
efficient, and remains so even when certain necessary nuisance functions such
as worst-case Q-functions are estimated at slow nonparametric rates. It is also
asymptotically normal, enabling easy statistical inference using Wald
confidence intervals. In addition, when certain nuisances are estimated
inconsistently we still estimate a valid, albeit possibly not sharp bounds on
the policy value. We validate these properties in numeric simulations. The
combination of accounting for environment shifts from train to test
(robustness), being insensitive to nuisance-function estimation
(orthogonality), and accounting for having only finite samples to learn from
(inference) together leads to credible and reliable policy evaluation.

在环境变化、干扰函数估计不一致和有限样本学习的情况下，本研究旨在评估策略值，并提出了一种扰动模型，可以根据转移观测对传统 MDP 进行边界估计。